Benitez-Paez et al. Movement Ecology (2021) 9:31 https://doi.org/10.1186/s40462-021-00268-4

METHODOLOGY ARTICLE Open Access Fusion of wildlife tracking and satellite geomagnetic data for the study of animal migration Fernando Benitez-Paez1,2 , Vanessa da Silva Brum-Bastos1 , Ciarán D. Beggan3 , Jed A. Long1,4 and Urška Demšar1*

Abstract Background: Migratory animals use information from the Earth’s magnetic field on their journeys. Geomagnetic navigation has been observed across many taxa, but how animals use geomagnetic information to find their way is still relatively unknown. Most migration studies use a static representation of geomagnetic field and do not consider its temporal variation. However, short-term temporal perturbations may affect how animals respond - to understand this phenomenon, we need to obtain fine resolution accurate geomagnetic measurements at the location and time of the animal. Satellite geomagnetic measurements provide a potential to create such accurate measurements, yet have not been used yet for exploration of animal migration. Methods: We develop a new tool for data fusion of satellite geomagnetic data (from the European Space Agency’s Swarm constellation) with animal tracking data using a spatio-temporal interpolation approach. We assess accuracy of the fusion through a comparison with calibrated terrestrial measurements from the International Real-time Magnetic Observatory Network (INTERMAGNET). We fit a generalized linear model (GLM) to assess how the absolute error of annotated geomagnetic intensity varies with interpolation parameters and with the local geomagnetic disturbance. Results: We find that the average absolute error of intensity is − 21.6 nT (95% CI [− 22.26555, − 20.96664]), which is at the lower range of the intensity that animals can sense. The main predictor of error is the level of geomagnetic disturbance, given by the Kp index (indicating the presence of a geomagnetic storm). Since storm level disturbances are rare, this means that our tool is suitable for studies of animal geomagnetic navigation. Caution should be taken with data obtained during geomagnetically disturbed days due to rapid and localised changes of the field which may not be adequately captured. Conclusions: By using our new tool, ecologists will be able to, for the first time, access accurate real-time satellite geomagnetic data at the location and time of each tracked animal, without having to start new tracking studies with specialised magnetic sensors. This opens a new and exciting possibility for large multi-species studies that will search for general migratory responses to geomagnetic cues. The tool therefore has a potential to uncover new knowledge about geomagnetic navigation and help resolve long-standing debates. Keywords: Animal migration, Data fusion, Earth’s magnetic field, GPS tracking, Swarm satellite constellation

* Correspondence: [email protected] 1School of Geography and Sustainable Development, Irvine Building, University of St Andrews, North Street, St Andrews KY16 9AL, Scotland, UK Full list of author information is available at the end of the article

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Background Migration studies now frequently use tracking data, Long-distance migratory navigation consists of two collected with in-situ locational devices (such as GPS parts, determining the direction of movement (through loggers) which record the location of animals during compass orientation) and geographic positioning, that is, their journeys. Tracking, combined with displacement, knowing where the animal is located at a specific time has become a common way of investigating a particular [1]. Both these mechanisms support the so-called true navigational cue (e.g. see [18] for an example of such an navigation, which is defined as finding the way to a far experiment for both geomagnetic and olfactory naviga- away unknown location using only cues available locally tion; some other examples include [20, 21]). Some stud- [2]. Compass orientation uses information from the Sun, ies have explored geomagnetic navigation by modelling the stars, the polarised light and the Earth’s magnetic potential migratory pathways based on real tracking data field [3, 4]. Positioning uses geomagnetism [3], olfactory and a static representation of the geomagnetic field [22]. cues [5, 6], and visual cues such as landmarks [7], while However, these fail to consider temporal variation in the another possible cue is natural and anthropogenic field, which may be problematic, as solar wind induced infrasound [1], although there are only a few studies on short-term variations of the geomagnetic field are this mechanism. It has been hypothesised that some ani- greater than the recorded magnetic sensitivity of migra- mals (birds, turtles, and fish) use sensory information tory animals. Neurophysiological experiments have from these cues to generate multifactorial internal maps shown that birds can sense changes in geomagnetic in- [7–9], although there is an on-going debate about the tensity between 50 and 200 nanoTesla (nT) [23, 24], and existence of such maps, as this is very difficult to con- behavioural experiments suggest sensitivity of 15-25 nT firm experimentally [2, 3]. [25]. Solar wind disturbances, however, can often reach One of the migratory strategies is geomagnetic navi- variations of over 1000 nT in polar latitudes within mi- gation [3], which uses information from the Earth’s nutes during geomagnetic storms [26]. That is, the field magnetic field for either compass orientation or geo- intensity changes across a very short period (seconds to graphic positioning or both. Various geomagnetic minutes) for over 1000 nT in the same location (not navigation mechanisms have been observed across across a spatial range, but in the same place). Migratory several taxa [3], from birds [1, 7], fish [9], sea turtles animals may therefore be impacted by such dynamic [8, 10], terrestrial [11, 12] and sea mammals [13, 14]. conditions. For example, looking specifically at birds, if In birds, for example, the strongest evidence for geo- they use the intensity value as a location marker, they magnetic navigation comes from studies that either may think they are suddenly somewhere else and could manipulate animal’s perceived magnetic position and try to compensate by changing their flight direction back observe their subsequent re-orientation towards mi- to their migratory corridor, as shown in virtual magnetic gratory destinations [15, 16] or those that surgically displacement studies [15–17, 27]. If the storm distur- manipulate animals’ organs that may help sense mag- bances are strong and come from many directions, this netic field, such as the trigeminal nerve. One study compensation could result in increased variation in [17] sections this nerve in Eurasian reed warblers and attempted flight directions. Alternatively, if they use dir- “virtually displaces” the birds using an artificial mag- ectional components of the field, such as inclination, netic field, then observes that the manipulated birds they may lose their compass sense and either change dir- are not able to correct their direction. Although see a ection or switch their navigation to other types of com- GPS study for the opposite finding in lesser black- passes that may be available at that particular location backed gulls [18]. In spite of decades of research, we and moment in time, e.g. a Sun or a star compass [4]. still do not fully understand how exactly animals use Other animals may react in different ways, depending on the information provided by the Earth’s magnetic field their particular manner of using the geomagnetic infor- toachievetruenavigation[1]. mation for navigation [3]. Indeed, geomagnetic storms Geomagnetic navigation has been studied with la- could be linked to large strandings of whales [13, 14], al- boratory experiments, which place animals in an arti- though this is not fully confirmed - see [28] for a coun- ficial magnetic field to study how the magnetic field ter argument. influences the direction of the onset of migration [2, Such effects would most likely be the highest during 7, 15, 17]. Such experiments provide precision and geomagnetic storms when the temporal variations of the control, but observed behaviour in such experiments field are the largest. To study how both long- and short- may differ from that observed in the wild [1]. A fur- term variation of the geomagnetic field affects migratory ther limitation is that these experiments focus on a navigation, we therefore need to obtain accurate values small number of individuals from one single species, of the geomagnetic field at the locations and times of which limits the generalisability of results across mul- animal passage. Satellite geomagnetic data, which pro- tiple species and taxa [19]. vide continuous global coverage, offer great potential for Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 3 of 19

this purpose, but there is currently no tool in existence generated through external influences [34]. The core that would combine these data with animal tracking field is generated by the geodynamo mechanism of the data. outer liquid core of the Earth, while the lithospheric field The process of combining multiple types of data is is created by the magnetic properties of the rocks in the commonly termed data fusion [29]. In animal migration Earth’s crust. External fields are caused by interactions research, tracking data are frequently combined with dy- with the Sun’s interplanetary magnetic field which pro- namic environmental data to account for navigational ef- duces electric currents in the ionosphere and magneto- fects that cannot be understood from tracking alone, sphere. On a large scale, the geomagnetic field is such as wind [30] or ocean circulation [31]. Contempor- approximately dipolar with the magnetic poles offset ary data fusion in movement ecology is primarily fo- from the rotation axis (Fig. 1a). However, in detail, it is cused on satellite imagery or modelled outputs (wind much more complicated with varying strength and angle and atmospheric models). For example, ENV-DATA across the globe (Fig. 1c). The field is measured in an [32], a popular movement ecology tool, supports the fu- Earth-based coordinate system, where the magnetic field sion of tracking data with a variety of satellite remote vector B is decomposed along the tri-axial North-East- sensing products. Ecologists also explore migration by Centre (NEC) system (Fig. 1b). The length of the field fusing tracking data with meteorological sources [30, vector B is the intensity F. The angle I between B and 33]. However, geomagnetic data have to date not been its horizontal component H is the inclination and the used, perhaps due to their inherent complexity: they are angle D between H and the geographic north (i.e. the N generated as three-dimensional time series of the mea- axis) is the declination. surements of the geomagnetic field at a specific location Earth’s magnetic field varies both spatially and tem- (either a terrestrial station or a satellite). This makes porally. Spatially, the intensity of the core field is be- data fusion with similarly structured tracking data (i.e. a tween approximately 23,000 nT at the Equator and 62, time series of observed locations) a geometrical chal- 000 nT at the Magnetic Poles, with geomagnetically lenge, specifically in terms of bridging the spatial and quiet time solar-induced variations of about 20 nT at temporal gaps between respective locations through ac- mid latitudes and 100 nT in polar regions [32]. During curate interpolation. geomagnetic storms, disturbances range over 1000 nT in In this paper we propose a new (and the first) method polar regions and 250 nT in mid latitudes [23]. These for spatio-temporal data fusion of wildlife tracking data changes can occur over periods of seconds to hours. with geomagnetic data from a satellite source (the Euro- Temporal variations of the total field are spread across pean Space Agency (ESA)’s Swarm constellation), which several components that vary across different time addresses the challenge of the spatio-temporal scales. Variations in the core field are called the secular interpolation between satellite and tracking data. This variation and are slow, mostly on time scales longer than will provide a possibility to combine satellite geomag- a year [34]. The lithospheric field is considered static on netic data with animal tracking data, something that has periods of less than a millennium. Rapid temporal varia- never been done before. Our method and its implemen- tions of the field (on timescales of seconds to days) are tation as a free and open source software (FOSS) tool linked to solar wind, which is a continuous emission of will therefore facilitate new lines of animal navigation re- ionised gas from the Sun that fills the interplanetary search which will be able to explore specific and exact space in the solar system [26]. Solar wind varies with the geomagnetic conditions that migratory animals experi- activity of the Sun and carries a magnetic field of solar ence during their journeys. origin, the Interplanetary Magnetic Field (IMF). When The rest of the paper is structured as follows: we first this reaches the Earth’s magnetosphere (the area around provide a short overview of relevant concepts, including the Earth that is filled with the geomagnetic field, Fig. the Earth’s magnetic field, its measurements and the use 1c), the magnetic field embedded in the solar wind con- of geomagnetic data in migratory navigation research. nects with the Earth’s magnetosphere, dragging field We then describe our new method and assess its accur- lines from day to night side into the magnetotail and acy. We further demonstrate the use of our tool on real driving electrical currents which travel to the surface of bird migration example and conclude with a discussion the Earth along field lines. When the solar wind is very on how our method could support new data-driven ini- strong or when the IMF has a particular orientation, the tiatives in research on animal migration. Sun’s magnetic field couples to that of the Earth and creates large disturbances of the geomagnetic field; these A short overview of concepts are known as geomagnetic storms. During such storms, Earth’s magnetic field is a constantly fluctuating combin- currents flowing in the magnetosphere and ionosphere ation of magnetic fields that originate from different intensify, creating auroral displays in high latitude re- sources: the core field, the lithospheric field and fields gions, and affect atmospheric density and satellite orbits. Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 4 of 19

Fig. 1 Components of the Earth’s magnetic field. a Orientation of the dipole field with respect to Earth’s rotation axis. b Measuring the field in the NEC coordinate system. B is the field vector, H its horizontal component, I the inclination and D the declination. c Earth’s magnetosphere is dynamically distorted by the solar wind carrying the Interplanetary Magnetic Field (IMF), which depresses the magnetosphere on the day side and extends its shape on the night side. Magnetosphere is the region of space around the Earth that is affected by its magnetic field. Bow shock marks its outermost boundary, where the speed of solar wind decreases. In magnetosheath, the Earth’s magnetic field is affected by the shocked solar wind and becomes weak and irregular. In magnetopause, the pressure from the Earth’s magnetic field and the solar wind are in balance - the size and the shape of magnetopause therefore constantly change in response to temporal variability in the speed, direction and strength of the solar wind. Magnetotail is the extended anti-sunward part of the magnetosphere: in reality the sphere is not a sphere (as in panel a) but has a large extended tail, created through the pressure of the solar wind

They also can interrupt our technology, such as radio quantifies local disturbances in the horizontal compo- communications and GPS signals through ionization. In- nent of the magnetic field in the range 0-9, with 0 de- tense bursts of high energy particles from the Sun asso- scribing calm conditions and values of 5 or more ciated with Coronal Mass Ejections can also cause describing a geomagnetic storm [26]. Values of local K- similar effects [34]. indices are aggregated into the 3-hour Kp index, which Real-time local disturbances of the geomagnetic field is a proxy for the energy input from the solar wind [35]. are represented with a set of geomagnetic indices. The Organised scientific measurements of the geomagnetic most common of these is the 3-hourly K-index, which field started in 1830s, picked up in earnest in the 1930s Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 5 of 19

[36] and have developed into a network of terrestrial gap that this paper attempts to fill: we develop the first magnetic observatories, the International Real-time data fusion tool that will allow ecologists studying migra- Magnetic Observatory Network (INTERMAGNET), tion to annotate their animal tracking data with accurate which currently includes 152 observatories [37]. Over measurements of the Earth’s magnetic field at the location the last 60 years, terrestrial measurements from INTE and time of migrating animals. This will, for the first time, RMAGNET have been complemented with measure- support exploration of contemporaneous animal re- ments from satellite missions [38] such as POGO (1965- sponses to field’s short-term variability. 1971), Magsat (1979-80), Ørsted (1999-present), CHAMP (2000-2010), SAC-C (2000-present) and most Methods recently the Swarm mission (launched in 2013) [39]. Our data fusion method (Fig. 2) combines dynamic geo- Terrestrial measurements, such as INTERMAGNET, are magnetic data with wildlife tracking data, where each advantageous because of high calibration accuracy, but tracked location is annotated with variables describing their spatial coverage is irregular (there are very few sta- the estimated state of the Earth’s magnetic field at that tions in the oceans and in remote continental regions). location and moment in time. The inputs into the In particular, measurements from one INTERMAGNET process are tracking data from a tagged animal and geo- station are applicable within around 1000 km of a magnetic data from the Swarm satellite constellation. ground station, but the only region where there is a suf- For each track location, we identify the nearest satellite ficiently dense network of stations to provide full cover- locations (we call these satellite points) in space and age for the whole area is northern and western Europe, time, i.e. those within a spatio-temporal kernel. We then which excludes the majority of animal migration path- calculate the spatial distance between the tracked loca- ways. Further, observatories submit their data to the tion point and the satellite point as the great circle dis- central network at different times and occasionally cease tance [46] and the temporal distance between the operation – resulting in a temporal lag of several years tracked location timepoint and satellite data. The great or occasionally missing data. Satellite missions, and in circle distance is the shortest distance between two particular Swarm as a multiple-satellite constellation, re- points on a sphere, where the path from one to another solve this problem as they provide consistent global is located on the surface of the sphere (see Supplemen- coverage, available within a few days of measurement. tary info 1 for more information). Satellite and terrestrial geomagnetic measurements are For each satellite point we obtain residuals between used to generate long-term models of the Earth’s magnetic raw measured values of the magnetic field and the mod- field [40] capturing the core and large-scale crustal mag- elled values of the field at that location, at the orbital netic fields; these models are used in navigation and refer- height. These residuals are at the centre of our method, ence systems. Geomagnetic data are also used to monitor as they represent the actual true variability of the field as short-term variations in space weather (including occur- influenced by the solar wind, which cannot be modelled rence of geomagnetic storms) and to predict potential but can only be measured in situ. For more information hazards to the terrestrial and satellite-based technological on how we calculate these residuals see the sub-section infrastructure [41]. Satellite and terrestrial geomagnetic on Calculation of magnetic components. data are open and accessible online – this includes both Residuals are interpolated using a Spatio-Temporal INTERMAGNET and satellite data, as well as K indices Inverse-Distance Weighted (ST-IDW) algorithm, which [35, 37, 40, 42]. In spite of their openness however, geo- prioritises measurements from satellite points that are the magnetic data are rarely used outside the specialist com- nearest to the tracked location in both space and time. munity. This may be because of their inherently complex The interpolated residuals are added onto the modelled structure (the Swarm data come as tri-axial time series of value of the magnetic field at the location of the tracking magnetic measurements for each of the three satellites in point and at altitude of the point (that is, we move the re- the constellation), a lack of interdisciplinary awareness on siduals from the orbital altitude to the altitude of the mi- what data are available, and/or lack of the technical skills grating animal). The result is a set of three magnetic required to obtain and use these data (e.g. they are pro- values in the NEC coordinate system at the location, alti- vided in unfamiliar data formats such as the binary Com- tude, and time of the tracked point, which are then used mon Data Format (CDF) developed by NASA [43]). to calculate other magnetic quantities (intensity F, inclin- In the context of migratory navigation, temporally vary- ation I, declination D and horizontal component H). In ing geomagnetic data are underused: migration studies the final step we also calculate error parameters for accur- typically limit themselves to either a static representation acy assessment. The process is repeated for all points in of the field [22] or model its long-term changes: in par- the tracking data and the result is an annotated track ticular the secular variation [44, 45], where the field where at each location we now have information on the changes over decades or centuries. There is therefore a corresponding geomagnetic conditions. Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 6 of 19

Fig. 2 A general outline of our magnetic annotation method. Green boxes show data inputs, blue boxes calculation steps and yellow boxes outputs

In the following we explain each of the steps in more Obtaining Swarm data detail, while mathematical derivations and technical de- The Swarm mission is a multi-satellite constellation op- tails are in Supplementary Information 1.Wealsode- erated by the European Space Agency with a goal to pro- scribe how we assessed the accuracy of our method and vide near-real-time data on the geomagnetic field and its present a practical example using real bird migration data. temporal dynamics [39] (Fig. 3). The constellation Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 7 of 19

Fig. 3 Orbits of the three Swarm satellites over a 24 h period (15 October 2014), A shown in 3D and B projected on the surface of the Earth. Measurements points are coloured according to the magnetic intensity F. (These images were created with the VirES web client https://vires.services/) consists of three identical satellites: named A(lpha), this by computing residuals between Swarm data and B(ravo) and C(harlie). A and C move in parallel sepa- values from a global geomagnetic model, which repre- rated by around 150 km as they cross the equator, flying sents the magnetosphere, core and lithospheric crust at a lower orbit of 480 km, while B orbits in a different fields [49]. That is, we take the measured field at the sat- drifting orbital plane at a height of 510 km and is, at ellite level and subtract modelled values from the same present, counterrotating to the A/C pair. All three satel- altitude (Fig. 4, residuals are shown in yellow, while the lites are equipped with identical instruments, including modelled values of the field at the satellite height are in the Absolute Scalar Magnetometer (ASM), Vector Field shades of brown/orange). Thus, Swarm residuals primar- Magnetometer (VFM) and a GPS Receiver. For technical ily represent the magnetic field variability induced by details of the Swarm mission see [39]. real-time solar-wind. We then calculate geomagnetic Swarm data are open and accessible online following values at the location and altitude of the migrating ani- the ESA Earth Observation Policy. We use Level 1b mal by adding these residuals to the core and crust products [47], which are the corrected and calibrated model values from this location (shown in blue/teal in outputs from each of the three satellites, provided in a Fig. 4), thus correcting for the strengthening of the core geocentric NEC reference frame. We use the MAGX_ and lithospheric field nearer their source. Note that we LR_1B product (Magnetic data, low rate), which is a consider the actual altitude of the tracked animal (for time series of three magnetic measurements in the NEC example a bird, as in Fig. 4) and do not assume that the system from each satellite, collected at 1 Hz resolution animal is on the surface of the Earth, since the intensity by the VFM and calibrated with the ASM and star- of the magnetic field falls off with altitude from the trackers. We also use the positional products Earth’s surface at around 20nT per km. This is not linear (GPSXNAV_1B, the on-board GPSR navigational solu- and varies with latitude, but the effect is captured by tion) to provide information on the location of all three taking the model at the altitude of the migrating animal satellites with 1 Hz resolution. A further product are (Z2 in Fig. 4). magnetic values from the CHAOS—7 model and the re- We use the CHAmp, Ørsted and SAC-C (CHAOS-7) spective residuals of the Swarm data to this model (see time-dependent geomagnetic model in this calculation next section for details). We access Swarm data through [50, 51], which is based on observations by Swarm, ESA’s Virtual workspace for Earth observation Scientists CryoSat-2, CHAMP, SAC-C and Ørsted satellites, and (VirES) client [48]. terrestrial observations from the INTERMAGNET net- work. Swarm residuals and CHAOS-7 model values are Calculation of magnetic components provided through VirES [52]. Swarm data provide information on the magnetic field at the altitude of the orbit, which is above the ionosphere, Spatio-temporal IDW interpolation where the geomagnetic field is affected by the electrical Swarm satellites move at around 7.8 km per second currents induced by the interaction of both sunlight, and along their respective orbits. In order to achieve suffi- the solar wind with Earth’s magnetosphere [34]. This cient interpolation quality at the varied locations of ani- means that to obtain the values of the magnetic field at mal tracking data, we must ensure that for each tracking the Earth’s surface where animals are migrating, the raw location we include a sufficient number of near-by satel- measurements from Swarm need to be corrected. We do lite points (that is, points at which there are satellite Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 8 of 19

Fig. 4 Using Swarm residuals to calculate real-time magnetic field at the altitude of migrating animal. We take the measured field at the satellite

height (Z1) and subtract modelled contributions of the core, crust and magnetosphere fields at this same height (orange/brown), to obtain the real-time solar-wind induced variability, represented as residuals (yellow). This variability varies at a much higher temporal scale than the

modelled contributions and can only be measured in situ. We then obtain modelled field values at the elevation Z2 of the migrating animal (values in blue/teal) and add residuals from height Z1, which gives us real-time field values at height Z2. All modelled values are from the CHAOS- 7 model [50, 51]. Charts are not to scale: the contribution of the core field typically represents over 98% of the total field measures and which are sufficiently close to the tracking orbits in 24 h). This means that the temporal distance point in space and time) to interpolate the magnetic between each two consecutive orbits of the same satellite values. For this, we define a spatio-temporal kernel at the Equator is approximately 1.5 h. Given that each around the tracking point, within which we search for orbit has an northward and a southward pass, which are satellite points. This kernel is defined in two steps separated by approximately 180o, this also means that (Fig. 5): one orbit counts for two crosses of the Equator, opposite each other. Since the A and C pairs of satellites orbit in I. Time-kernel: we select points from all three Swarm parallel with a delay of a few seconds and the orbit of B satellites within the +/− 4 h window around the is currently almost perpendicular, this means that there respective tracking point. are four relatively equally spaced intersections of the II. Space-kernel: from among the temporally-selected Equator for each orbit. These intersections are displaced points, we select those that fall within a circle for approximately 667 km with every subsequent orbit centred on the tracking point. (i.e. 40,075 km/(15 × 4)). Based on this, a circle with a ra- dius of 1800 km on the Equator and a temporal window The choice of the parameters for the spatio-temporal of +/− 4 h from the trajectory point ensures a selection kernel was based on the orbital properties of Swarm. of a minimum of 2-3 satellite points for each location on The radius of the circle in the space kernel was deter- the surface of the Earth at any time. Since the orbits are mined based on the equatorial circumference of the polar orbits and therefore converge near the poles, we Earth (40,075 km) and the number of orbits of each decrease the circle radius with latitude to 900 km at both Swarm satellite in 24 h (each satellite completes 15 Poles (Fig. 5A).

Fig. 5 Selection of Swarm points. A The spatial extent of the spatio-temporal kernel varies with latitude, with larger circles on the Equator and smaller towards the Poles. B Spatio-temporal kernels shown in a space-time cylinder (note that in this display, the third dimension is time), demonstrating the calculation of the spatio-temporal weights (details in Supplementary Information 1). C The spatio-temporal kernel allows us to select the nearest Swarm points to the tracking point Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 9 of 19

Once satellite points are selected, we obtain respective the minimum and average spatial distances from the tra- residuals (see section on Magnetic components above) jectory point to the set of satellite points and the average at each satellite point and interpolate these with spatio- Kp index at the location and time of the tracking point. temporal inverse distance-weighting (ST-IDW). That is, The process is repeated for each point in the tracking we take residual values from all satellite points and data. interpolate across space and time to obtain residual values at the location of the tracking points. We do this Accuracy assessment using the following procedure: for every satellite point To assess the accuracy of our data fusion procedure, we within the spatio-temporal kernel we compute two mea- compare our interpolated geomagnetic values with cali- sures: i) the spatial distance between the tracking point brated magnetic measurements from the INTERMAG and the satellite point as a great circle distance (ds; Fig. NET network (Fig. 6)[37]. INTERMAGNET stations 5B, the great circle distance is the shortest distance be- provide data products at different temporal resolutions. tween two points on a sphere, see Supplementary infor- We use the quasi-definitive data, which is a time series mation 1 for mathematical details), and ii) the time of absolute values of the magnetic field, provided at the distance between the tracking point and the satellite resolution of 1 min [53]. These data have an error of ap- point (dt; Fig. 5B). The spatial and temporal distance are proximately 5nT, depending on the quality control pro- combined into a spatio-temporal distance, which is nor- cesses at an observatory, but are made available at near malised and inverted to create the weight for real-time. We have chosen quasi-definitive data over the interpolation. Interpolated residuals are added to the definitive product (the absolute values of the field with modelled values at the location, altitude and time of the full corrections for instrument drift, error < 1nT) as they tracking point to create real geomagnetic measurements are available within 72 h of observation, while the defini- in the NEC directions at this location and moment in tive product are often not available for a year or more. time (Fig.5C ). We note however that the spatial part of Given the lower limit of what animals can physiologic- the interpolation is done across a 2D surface, that is, it ally sense (20nT [25]), using quasi-definite data is suffi- only considers the horizontal spherical distance between cient for our purpose. the GPS point and the satellite points and not the differ- We obtained INTERMAGNET data from three obser- ence in altitude. This may introduce a source of error, vatories and three temporal periods with different levels especially in the part of the residual field originating in of geomagnetic activity, which is a common way to as- ionospheric currents flowing below the satellites but sess how magnetic interpolation methods perform under above the elevation of migrating animals. varied conditions [54, 55]. Our goal was to assess how In the final step, we annotate the tracking point with the accuracy of our method varied with: i) the level of the resulting NEC magnetic values and other computed disturbance in the geomagnetic field at that location and magnetic quantities (the intensity F, the horizontal com- time, ii) the latitude of the tracking location, and iii) the ponent H, the inclination I and the declination D). For parameters related to the spatio-temporal kernel (i.e., each tracking point we also calculate parameters related the number of selected satellite points and the minimum to interpolation accuracy – these include the number of and average spatial distance from the trajectory point to Swarm satellite points within the spatio-temporal kernel, the respective satellite points). The level of activity was

Fig. 6 Map of INTERMAGNET observatories showing locations of the three that we selected for accuracy assessment (given with their observatory codes, Lerwick – LER, Hartland – HAR, Pedeli – PEG) Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 10 of 19

defined using the global Kp and local K index (Table 1). geomagnetic disturbance are larger in higher latitudes. We chose INTERMAGNET observatories at three differ- We therefore used the station at the highest latitude ent latitudes (Fig. 6): Lerwick (LER, UK; 60.1° latitude, − (LER) as the baseline in the GLM. 1.2° longitude), Hartland (HAD, UK; 51° latitude, − 4.5° longitude), and Pedeli (PEG, Greece; 38.1° latitude, 23.9° Practical example: is migratory movement of greater longitude). white-fronted geese affected by geomagnetic storms? We obtained one-minute magnetic measurements To illustrate a new type of biological question that can from all three stations for three 48-h periods, each with be answered using annotated data from our tool, we ex- a different level of geomagnetic activity (Table 1). We in- plore the hypothesis that migratory movement is af- terpolated the Swarm geomagnetic values for each sta- fected by local geomagnetic conditions. The novelty of tion location across the same time-frame using our this example is that the conditions that we study are method. We then calculated the error as the difference local, that is, they occur at the location and time of each between the interpolated values of intensity F and the individual - we study this using the local Kp indices INTERMAGNET values (ground truth). We chose to ex- from our annotated data. Previous studies used global plore the error in intensity only, since calculating errors geomagnetic indices (for example, [56] used global Ap for each individual axis would require knowledge of the indices, which give a maximum disturbance anywhere orientation of the sensor on the animal tag, which would on the planet), meaning that there is one value that de- need input from additional sensors (such as an acceler- scribes the geomagnetic conditions anywhere on Earth, ometer or a north-seeking gyrometer) and which may and there is no way of knowing if those conditions actu- not be available in tracking data from tags that only pro- ally occurred at the location and moment in time we are vide GPS measurements. interested in. However, geomagnetic storms are local We used a log-link Gaussian generalized linear model events, in the sense that the field is disturbed unevenly (GLM) to assess how different levels of absolute error of in both space and time, depending on the fluctuations of intensity varied with parameters associated with the the solar wind - a global index aggregates this into one spatio-temporal kernel and with the local level of geo- value for the entire planet [42]. In contrast, our tool pro- magnetic disturbance (the K index from each station, vides this information locally: by annotating tracking Table 1). We further controlled for the observatory, first data with real time local geomagnetic information, we because the data are collected in different ways at each can find out where and when each individual encoun- station and second, because the effects of the tered stormy conditions. This lets us explore, for the first

Table 1 Geomagnetic activity at three INTERMAGNET stations (LER, HAD, PEG) selected for accuracy assessment Disturbed period Medium-disturbed period Quiet period Interval (hours) LER HAD PEG Kp LER HAD PEG Kp LER HAD PEG Kp 22-Jun-2015 0 1 1 2 07-Mar-2015 3 3 3 4 09-Mar-2015 3 3 3 3 0 - 3 23 3 3 33 3 4 12 1 23-6 34 4 4 13 2 3 01 1 06-9 2 3 NA 3 2 3 3 3 0 0 1 0 9 -12 45 4 5 23 3 3 01 1 112-15 5 5 5 6 3 4 4 4 0 1 1 1 15 -18 7 8 8 8 3 4 4 3 0 0 1 0 18 -21 64 5 6 44 4 3 01 1 121-24 23-Jun-2015 8 5 6 7 08-Mar-2015 2 3 2 3 10-Mar-2015 1 1 1 1 0 - 3 85 5 8 12 2 2 01 1 13-6 75 5 6 22 1 2 11 1 26-9 5 4 NA 5 2 3 2 3 1 1 1 1 9 -12 45 4 5 33 3 3 01 1 012-15 2 3 3 3 1 2 2 2 0 1 0 0 15 -18 2 4 4 4 2 2 2 2 1 1 1 1 18 -21 33 3 4 01 0 1 00 1 121-24 Table shows local K indices for each of the three stations in each 3-h slot as well as the planetary global Kp index for the same time period. 3-hourly periods with no data (NA) were excluded from consideration Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 11 of 19

time, the link between actual local conditions and prop- We then further removed all points where geese were erties of movement. stationary, by selecting locations with speed higher than We study the North Sea population of the greater 5 km/h. This is a reasonable choice to isolate data col- white-fronted geese (Anser albifrons)[57, 58], which mi- lected during flight, as the highest running speed for grate between northern Germany and the Russian Arc- geese was found to be 1.17 m/s or 4.21 km/h [60]. tic. Our hypothesis is that when geese encounter highly Greater white-fronted geese spend the majority of au- disturbed geomagnetic conditions (as demonstrated by tumn migration in stopover sites [61], so once stationary the local Kp index being more or equal to 5, which is points were removed, this left us with 13,697 points of the cut-off for a geomagnetic storm [26]), their move- migratory movement. For each of these remaining ment is disturbed and this will be reflected in corre- points, we assessed if it was collected during a geomag- sponding movement data. We explore this hypothesis by netic storm: the points where local Kp was higher or analysing two movement properties (speed and turning equal to five were marked as occurring during a storm. angle) at each location on the geese tracks, during geo- This resulted in 312 migratory movement points taken magnetic storms and during quiet periods. during a storm and 13,385 points during quiet geomag- We used data from a published study [57, 58] from a netic conditions. Both storm and non-storm points single autumn migration (1 Aug 2017 to 15 November belonged to all 22 individuals. In the final step we statis- 2017) of 22 individuals with a total of 151,156 GPS loca- tically analysed the distribution of speed and turning tions. As white-fronted geese stay in families or pairs the angle values during the stormy and quiet conditions, to whole year round and migrate in these groups [58], we assess if we could identify any differences in these two only used tracks from individuals which did not migrate movement parameters. Specifically, we used standard together, to ensure independence of data. We chose this statistics measures for analysis of segment duration and migration because autumn 2017 was geomagnetically speed and circular statistics measures for analysis of very active, with some of the strongest geomagnetic turning angles. storms of the 24th solar cycle (2008-2019). A particu- larly strong storm occurred on 7-8 Sept 2017, with sig- Tool and data availability nificant effects in the north of Russia [59] – the same Our method was implemented using Python 3 in the area where our geese were situated at approximately the Jupyter notebooks environment [62]. The code is pro- same time. vided as Supplementary Information 2 and available at Geese tracks were first annotated with geomagnetic GitHub repository MagGeo (https://github.com/ values using our new tool. Given our data were in MagGeo/MagGeo-Annotation-Program, continuously WGS1984 long/lat system, all distances and angles were updated version) or through Zenodo (doi: https://doi. calculated in spherical geometry, as great circle lines (see org/10.5281/zenodo.4543735, version from 21 Feb 2021). Supplementary Information 1). We first calculated the Our tool uses two specific Python packages: the ESA- speed and the turning angle at each location. Speed was VirES Client [63], which connects to the VirES server calculated based on the great circle distance between and handles downloads of Swarm data, and the chaos- two consecutive GPS points forming a track segment magpy package [64], which provides access to the and the duration of the segment (time distance between CHAOS model (presently at version 7). We used the the two GPS points, given in seconds) and assigned to move R package [65] for movement analysis in the prac- the first point of each segment. Turning angle was calcu- tical example. lated as the angle between two consecutive segments Swarm data were obtained through the VirES client (i.e. using three consecutive GPS points on the track), [48] and INTERMAGNET data are available at [53]. where the angle was measured on the surface of the Data on geomagnetic indices at INTERMAGNET sta- sphere between the two segments as great circle distance tions were obtained from [35, 66]. Case study data on lines. The angle was assigned to the location that migration of great white-fronted geese are published on belonged to both segments (i.e. to the middle of the Movebank [57, 58]. three GPS points). In order to ensure that the potentially unequal duration of the two consecutive segments would Results not affect the calculation of the turning angles, we also Accuracy assessment removed all points where segment duration was more The error in magnetic intensity F (jointly across the than 30 min (1800s). As we were only interested in mi- three observatories) had a mean of − 21.6 nT (black gratory journeys, we removed non-migratory GPS points dashed line in Fig. 7A) with a 95% CI [− 22.26555, − in two steps. We first removed points from summer and 20.96664]. The distribution of error was concentrated winter sites by, for each individual, deleting points which between − 50 nT and + 50 nT (the red dashed lines on were within 200 km of its extreme NE and SW corner. Fig. 7A show the 2.5 and 97.5 percentiles), but exhibited Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 12 of 19

Fig. 7 Error in magnetic intensity (F). A shows the distribution of the error for all three observatories and the black dashed line indicates the mean error = − 21.61, with a 95% CI [− 22.26555, − 20.96664]. The two red dashed lines show the 2.5 and 97.5 percentile of the distribution. B shows the probability density and distribution of error values per station. C shows a scatterplot of the absolute error against the K index and the curve of best fit for each observatory (Lerwick, Hartland, Pedeli) negative skewness (γ = − 3.86) owing to a few high nega- distance from the satellite points to the tracking point tive values (Fig. 7A). The distribution of errors by station and the local level of the geomagnetic disturbance given (Fig. 7B) shows that the very large and negative errors by K index. We also included a control variable for the are at the station at the highest latitude (Lerwick). effect of the IMO observatory, which served as a proxy On average, we either underestimate or overestimate for latitude (our baseline was LER, which is the observa- by a small amount (~ 20-50 nT) at each of the three sta- tory in Shetland, at the highest latitude among our three tions. This small bias away from zero can be ascribed to locations). We first removed highly correlated variables unmodeled lithospheric field which is not captured by (those with r > 0.7): specifically, the average spatial dis- the CHAOS model. We found the error increased with tance of all satellite points to the trajectory point was the presence of geomagnetic storms (defined by the local correlated with the minimum distance and the total K index; Fig. 7C). Here we found that the absolute error number of satellite points and was subsequently re- increases logarithmically for Lerwick but linearly at moved from analysis. The final model (pseudo R2 = 0.52) Hartland and Pedeli (Fig. 7C), which is a latitudinal ef- included the following variables: the minimum spatial fect related to the proximity of Lerwick to the auroral distance to satellite points, the total number of satellite region. points, the IMO observatory variable, and the local geo- We explored the relationship between the absolute magnetic activity index (K). error of intensity and location and method-related pa- Both the total number of points (β = − 0.043, p < 0.01) rameters with a log-link Gaussian GLM model. Specific- and the minimum spatial distance to satellite points (β = ally, our independent variables included the number of − 0.001, p < 0.01) were significant predictors of error satellite points, the minimum and the average spatial (Table 2). Each additional satellite point is associated Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 13 of 19

Table 2 Log-link Gaussian GLM model using absolute error as p < 0.01, percent effect = 123.38) and PEG (β = 1.812, the dependent variable p = < 0.01, percent effect = 512.29) suggested that the β Std Err exp(β) [exp(β)-1]×100 absolute error changes with the observatory. We further Total Points −0.043* 0.001 0.95778 −4.22 found that higher K values (β =0.419, p = < 0.01, percent Station (Ref. Lerwick) effect = 52.07), which indicate disturbed conditions, were Hartland 0.804* 0.046 2.2338 123.38 associated with higher levels of absolute error compared Pedeli 1.812* 0.034 6.1229 512.29 to periods with lower K values (during geomagnetically quiet conditions). We also found that higher K values are K index 0.419* 0.002 1.5207 52.07 associated with higher error at higher latitudes (ref = Ler- Min. Distance −0.001* 0.00002 0.9992 −0.08 wick:K) than at mid- (Hartland: K, β = − 0.272, p <0.01, Interaction (Ref. Lerwick:K) percent effect = − 23.81) and lower latitudes (Pedeli: K, Hartland:K −0.272* 0.0005 0.7618 − 23.81 β = − 0.320, p < 0.01, percent effect = − 27.36). Pedeli:K −0.320* 0.035 0.7263 −27.36 Intercept 2.734* 0.035 15.3973 Practical example: is migratory movement of greater white-fronted geese affected by geomagnetic storms? Observations 19,950 Figure 8 shows a map of the tracks that were used in Log Likelihood −95,278.82 analysis. Locations where individuals encountered geo- Akaike Inf. Crit. 190,573.6 magnetically stormy conditions during flight are shown McFadden’s pseudo R2 0.52 in red. For each predictor we provide the regression coefficient (β), the standard Figure 9 shows statistical distributions of the segment error, exp.(β), and the percent effect size ([exp(β)-1]×100) duration (time between two consecutive GPS fixes), *p < 0.01 speed and turning angle values during geomagnetic storms (panels A, C, E) and during quiet conditions with an absolute error decrease of 4.22%, while each (panels B, D, F). Since duration of segments could po- kilometre increment in the minimum distance is associ- tentially affect the calculation of turning angle, we first ated to a 0.08% absolute error decrease. When con- compared the two distributions of respective durations trolling for observatories by comparing to the baseline (panels A and B), which are very similar with the mode at LER, the regression coefficients for HAD (β =0.804, value of 300 s (5 min) for both distributions. We found

Fig. 8 Map showing migration tracks of 22 great white-fronted geese during 2017 autumn migration. Locations where individuals encountered geomagnetic storm conditions (local Kp > =5) during flight are shown in red. Map was created using the Albers equal area projection Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 14 of 19

Fig. 9 Distribution of movement parameters during and outside of geomagnetic storms. Panels A and B show the distribution of segment durations for storm (A) and no storm (B) – the most common duration in both cases is 5 min (300 s). Panels C and D show distribution of speed during stormy conditions (C) and during quiet conditions (D). Panels E and F show distributions of turning angle values during stormy (E) and quiet conditions (F). In these two panels, the 0 reference is the bearing obtained from the previous and current GPS points that the two means (341.93 s (%95 CI [322.07, 361.79]) CI [43.20, 44.17]) and 28.82 km/h. The difference between and 351.77 s (%95 CI [348.37, 355.16]) for storm/no mean speed during quiet and storm periods was not sig- storm data) and standard deviations (178.28 s and nificant (Welch t-test [67], p = 0.23), but speed variances 200.54 s for storm/no storm data) were not significantly were significantly different (Levene test, p <0.001). We different from each other (t-test [67] for means, p = 0.16, used the lawstat R package [68] for Levene test. Levene test [68] for stDev, p = 0.30). We therefore as- The mean turning angle during storms (μcirc = 6.76°, sume that since the segment length distributions are %95 CI [6.67, 6.85]) was significantly different from the similar, they affected the calculation of the turning angle mean turning angle during quiet conditions (μcirc = − 0.35°, in a similar way for data collected during the geomag- %95 CI [− 0.34 -0.36]; Watson’s large-sample non- netic storms and those from quiet conditions, which parametric test [69, 70], p = 0.003). We also found that the makes turning angles from both cases comparable. angular standard deviations (a measure of angular concen- The mean and standard deviation of speed in stormy tration) of turning angles for storm (σcirc = 1.03) and quiet conditions were 42.27 km/h (%95 CI [38.50, 46.05]) and conditions (σcirc = 0.92) were significantly different 33.87 km/h respectively, compared to the mean and (Wallraff’s non-parametric test [71], p = 0.001). Finally, standard deviation in quiet conditions: 43.68 km/h (%95 there is further evidence that the two samples of turning Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 15 of 19

angles (quiet vs. storms) were not drawn from a common researchers to ask and answer questions that have so circular distribution (Watson’s two-sample U2 test [72], far been unanswerable with existing methods and data p < 0.001). All circular tests were performed using the sets. circular package in R [73] and the methods described by In the following we discuss some advantages and limi- Pewsey et al. [74]. tations that we encountered in the process of developing These results suggest that, in this data set, movement our data fusion tool, outline recommendations for use during geomagnetic storms could have been affected by and present ideas for future developments. local disturbed conditions of the magnetic field. Specific- One of the main advantages of this work is that this is ally, we may see an effect on the choice of direction at the first time that satellite geomagnetic data have been each point, since on average during storms turning made accessible to movement ecologists. These data are angles seem to tend 6.76o towards the right, rather than complex to use due to their structure as a time series of straight ahead as in non-stormy conditions. Given the tri-axial measurements taken at satellite locations at or- general direction of migration from NE to SW, this bital altitude - combining these with similarly complex means that the birds are being displaced towards the tracking data poses a specific geometric challenge that north. A further effect is on the choice of turning angles, our new method successfully resolves. In addition, satel- since these birds tend to choose a wider range of more lite geomagnetic data are less accessible outside geo- randomly distributed angles during the storms than in physics due to the format used for their publication, the quiet conditions (as shown with a significantly larger Common Data Format (CDF), which was created by standard deviation of angles during stormy conditions). NASA in 1985 [43]. This format is binary and not recog- The effect on speed is present in terms of higher stand- nisable by data analysis software commonly used in ard deviation, but not the mean speed. It is beyond the ecology (such as the R environment for statistical com- scope of this paper to speculate on reasons of why we puting). Through resolving both these two issues (i.e. see these effects, based on this small example. However, geometric complexity and unusual data format), our this small case study demonstrates how geomagnetic Python tool therefore provides, for the first time, an op- effects can now be explored with real time local data portunity for interdisciplinary secondary use of satellite and how our tool can support such analyses. geomagnetic data and through this opens new possibil- ities for data-driven investigation of animal migration. Another advantage of our method is that while it is Discussion demonstrated using GPS tracking data, it can be used This paper introduced a new method for spatio- with any kind of tracking data used in ecology, such temporal data fusion of wildlife tracking data and satel- as Argos data, data from VHF radio-tracking or from lite geomagnetic data. We developed the new fusion light-loggers. Non-GPS based tracking systems typic- methodology, implemented it as a FOSS tool, evaluated ally have a higher degree of spatial and/or temporal its accuracy and demonstrated the use on a case study uncertainty, and these uncertainties may impact the with real wildlife tracking data. definition of the spatio-temporal kernel. For example, The practical case study demonstrated how we can Argos data provide estimated error ellipses for each address new biological questions about real time re- locational fix [75] and this ellipse could be used as sponses to geomagnetic conditions, which require the 2D basis of the spatio-temporal kernel instead of linked locational and geomagnetic data through prox- the circle as in our method. imity in space and time and which were previously Geomagnetic field varies not only by geographic lo- unanswerable. Our case study is the first time that cation and time, but also by altitude: contributions of anyone has been able to study how contemporaneous the core and lithospheric fields are stronger at the and co-located highly dynamic geomagnetic condi- surface than higher up in the atmosphere. This means tions influence migratory movement of birds. The re- that aerial species that migrate at higher altitudes (for sults of our case study suggest that there may exist example, bar-headed geese fly over the Himalayas at an immediate effect of the geomagnetic disturbance altitudes of over 6000 m [76]) will experience slightly on the choice of direction. However, this is a very different geomagnetic conditions than those at the sea small example and as such it does not provide suffi- level. Our tool addresses this by adding Swarm resid- cient evidence for a more general conclusion. What is uals onto the CHAOS-7 model values at the location important, however, is that this case study demon- and altitude of the tracking point. This however re- strates what is now possible: our tool supports new quires accurate measurements of altitude in wildlife analyses of animal navigation in response to contem- tracking data, which are often not captured as accur- poraneous geomagnetic conditions at the precise loca- ately as horizontal coordinates, or not captured at all tion where the animal finds itself, and allows – in such cases, the tool defaults to creating values of Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 16 of 19

the geomagnetic field at an altitude of zero metres would produce highly accurate results. For migratory above the WGS-84 ellipsoid. studies, a recommendation is to be aware of this and ex- The exploratory analysis of the errors produced by our ercise caution when using our tool on data on days method indicate a small but systematic bias (mean of ab- when geomagnetic storms occur. solute error = − 21.61 nT) of the geomagnetic intensity Accuracy might be further improved by changing the which varies by station due to unmodeled contribution parameters of the spatio-temporal kernel or using a dif- from the local lithospheric field. The offset is small com- ferent interpolation scheme that would better reflect pared to the actual values of intensity (e.g. 55000nT at how the geomagnetic field changes across both time and LER) and disturbance variability (e.g. 1000nT at higher geographic space. In our ST-IDW interpolation we as- latitudes) though could potentially be larger over certain sume an isotropic change of the field. However, there types of geology like volcanic islands. In terms of using are differences in how the field varies in North-South our tool for analysis of animal migration, this means that and East-West directions [55]: for example, ionosphere we would be able to identify if migratory animals reacted is persistent over 1000 km in East-West direction and to lower or higher levels of the intensity, but because of 800 km in the North-South direction. This could be inte- the generally unknown bias we would not be able to spe- grated into our method, for example by either changing cify the absolute level of the local magnetic field to the form and size of the spatio-temporal kernel (e.g. which animals responded. However, this average field using an ellipse for its base rather than a circle) or by error is at the lower level of the minimum intensity that prioritising weights in a particular direction. animals can sense (20-200nT, [23–25]). For this reason A further issue is the estimation of the ionospheric and since compass and map navigation strategies depend part of the geomagnetic field, which contributes to its on patterns in geomagnetic values rather than on abso- daily variation. This part of the total field is generated by lute values (e.g. a constant bearing for the compass), the large solar-induced currents in ionosphere (the region of magnitude of our error offset is unlikely to pose a prob- 60-1000 km above the Earth’s surface), which vary with lem in migration studies. altitude (there are different currents in different regions By fitting the log-link Gaussian GLM to the absolute of the ionosphere), latitude and time of the day (currents error we found that the best model representing our are stronger on the day side of the Earth than on the error had a moderate R2 (0.52). This suggests that there night side) [26]. Due to complex variation of the induced are either other factors which affect the error, such as currents, these ionospheric contributions are highly tem- the limited availability of Swarm data in any given time- porally dynamic and difficult to calculate without actu- space window or the size of the window. Further analysis ally measuring the field. In our case, the ionospheric of the error structure in our interpolation is potentially contribution at satellite altitude is present in Swarm re- useful, but would require ground truth data from more siduals, and we do not correct for this contribution than just three INTERMAGNET stations – this has not when we transfer weighted residuals to a lower altitude. been possible in for this study as we were only able to The reason for this is that modelling the ionospheric obtain data on local K indices for three stations (i.e. only contribution on the ground is very complex. While Vi- a few stations provide local K indices continuously). We rES for example provides an empirical model of the as- still observe a statistically significant difference between sociated magnetic field of the ionospheric current observatories, which is likely linked to differences in system [48], such models do not work well at higher lati- latitude and the proximity to the auroral oval whose tudes and not at all during times with high geomagnetic position can vary rapidly over tens of minutes. activity. We have therefore opted for a computationally One of the main predictors of the level of error is the simpler solution, which introduces an additional error to K index, which is a measure of the geomagnetic storm our final values. Given the high temporal variation of the activity. Our accuracy assessment suggests that a higher ionospheric contribution however, this error is mini- K index results in lower accuracy, especially in higher mised through our spatio-temporal weighting of resid- latitudes. This is reasonable and in agreement with the uals, which down-weighs residuals that are far from the polar-orbiting design of the Swarm constellation, which GPS point in space and time. Additionally, and as dis- provides denser coverage at higher latitudes where geo- cussed above, while the error due to ionospheric contri- magnetic intensity and variation happen to be higher. bution is still present, the accuracy of our method is This variation in accuracy with latitude and geomagnetic sufficient in the context for which the tool was built, disturbance should be considered when using these data, that is to study animal responses to the geomagnetic especially when the local K index is 5 or higher (Fig. field. 6C). Nonetheless, between 1995 and 2014, less than 5% A final limitation is demonstrated in the case study, of days were geomagnetically disturbed with Kp > 5 [77]. where a proportion of GPS points could not be anno- This indicates that for 95% of the days our method tated due to lack of Swarm data. This occasionally Benitez-Paez et al. Movement Ecology (2021) 9:31 Page 17 of 19

occurs due to issues of satellite maintenance, orbital re- Availability of data and materials calibration, or other engineering reasons. A list of miss- Data: Swarm data were obtained through the VirES client [48] and INTE RMAGNET data are available at [53]. Data on geomagnetic indices at INTE ing data periods is regularly published on the Swarm RMAGNET stations were obtained from [35, 66]. Case study data on website [78]. A solution would be to incorporate data migration of great white-fronted geese are published on Movebank [57, 58]. from other geomagnetic satellites which are currently in Code: Our method was implemented using Python 3 in the Jupyter notebooks environment [62]. The code is provided as orbit (for example, a Chinese mission called CSES and a Supplementary Information 2 and available at GitHub repository MagGeo Canadian satellite called Cassiope/ePop). This would (https://github.com/MagGeo/MagGeo-Annotation-Program) or through also potentially result in more satellite points within the Zenodo (doi: https://doi.org/10.5281/zenodo.4543735). Our tool uses two specific Python packages: the ESA-VirES Client [63], which connects to the Vi- spatio-temporal kernels, thus further improving the rES server and handles downloads of Swarm data, and the chaosmagpy accuracy. package [64], which provides access to the CHAOS model (presently at ver- sion 7). Conclusions Declarations To conclude, our new data fusion method of wildlife tracking and satellite geomagnetic data provides ecolo- Ethics approval and consent to participate gists, for the first time, with an opportunity to explore No ethical issues arose in this work. how migratory animals react to specific geomagnetic conditions. This opens a new and exciting possibility for Consent for publication Not applicable. large multi-species data-based approaches that will search for general migratory responses to geomagnetic Competing interests cues and re-use tracking data that have already been col- The authors declare that they have no competing interests. lected, without requiring to start new expensive tracking studies using trackers with magnetic sensors. With the Author details 1School of Geography and Sustainable Development, Irvine Building, on-going data revolution in bio-logging, based on mini- University of St Andrews, North Street, St Andrews KY16 9AL, Scotland, UK. aturisation of devices and new tracking systems dedi- 2The Alan Turing Institute British Library, England, London, UK. 3British cated to animal movement research, such large multi- Geological Survey, Research Ave South, Riccarton, Edinburgh, Scotland, UK. 4Department of Geography and Environment, Western University, London, species data experiments are becoming essential to build Ontario, Canada. new knowledge on animal migration. Our data fusion method supports these new studies by providing links to Received: 18 January 2021 Accepted: 30 May 2021 satellite geomagnetic data that would not be accessible to ecologists otherwise and may thereby help resolve References some of the big debates about geomagnetic navigation. 1. Deutschlander ME, Beason RC. 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